The ElectronVolt: Videos & Practice Problems

In the context of electric potential and energy, the electron volt (eV) is a unit representing the change in potential energy of an electron moving through a potential difference of 1 volt. The relationship between potential energy change (ΔU) and potential difference (ΔV) is given by the equation $\mathrm{\Delta U}=q\times \mathrm{\Delta V}$. For kinetic energy calculations, the formula $\mathrm{KE}=1/2mv^2$ is used, where m is mass and v is velocity. Understanding these concepts is crucial for analyzing particle behavior in electric fields.

The ElectronVolt

In the study of electric potentials and potential energy, the concept of the electron volt (eV) is crucial. An electron volt is defined as the amount of energy gained or lost by an electron when it moves through a potential difference of one volt. To understand this, consider two charged plates with a potential difference of 1 volt. When an electron, which carries a charge of negative elementary charge (−e), moves from the negatively charged plate to the positively charged plate, it experiences a change in potential energy.

The relationship between potential energy change (ΔU), charge (q), and potential difference (ΔV) is given by the equation:

$$\Delta U = q \cdot \Delta V$$

For an electron moving through a potential difference of 1 volt, the change in potential energy can be expressed as:

$$\Delta U = -e \cdot 1 \text{ V}$$

Substituting the value of the elementary charge, which is approximately \(1.6 \times 10^{-19}\) coulombs, allows us to calculate the change in potential energy in joules. As the electron moves, its potential energy decreases, converting into kinetic energy, which results in an increase in speed.

Conversely, a positive charge, such as a proton, would move in the opposite direction, from the positive plate to the negative plate, and would experience a negative potential difference when moving left. The same equation applies, but the signs of the charge and potential difference must be carefully considered to determine the change in potential energy.

The electron volt serves as a convenient unit for measuring energy at the atomic and subatomic levels. For example, if an electron has a kinetic energy of 100 eV, this can be converted to joules by multiplying by the elementary charge:

$$\text{Kinetic Energy (J)} = 100 \text{ eV} \times 1.6 \times 10^{-19} \text{ J/eV} = 1.6 \times 10^{-17} \text{ J}$$

To find the speed of the electron, we can use the kinetic energy formula:

$$KE = \frac{1}{2} m v^2$$

Rearranging this gives:

$$v = \sqrt{\frac{2 \cdot KE}{m}}$$

Substituting the kinetic energy in joules and the mass of the electron (approximately \(9.11 \times 10^{-31}\) kg) into the equation allows us to calculate the speed. For instance, if the kinetic energy is \(150 \text{ eV}\), converting this to joules and substituting into the formula yields a final speed of approximately \(7.26 \times 10^6\) meters per second.

In summary, the electron volt is a vital unit in physics, particularly in the context of electric potential and energy transformations, allowing for straightforward calculations involving small charges and their kinetic energies.

Here’s what students ask on this topic:

What is an electron volt (eV) and how is it defined?

An electron volt (eV) is a unit of energy commonly used in the field of atomic and particle physics. It is defined as the amount of kinetic energy gained or lost by an electron when it moves through an electric potential difference of 1 volt. Mathematically, it is given by the equation:

$\mathrm{\Delta U}=q\times \mathrm{\Delta V}$

where $\mathrm{\Delta U}$ is the change in potential energy, $q$ is the charge of the electron (approximately $1.6\times {10}^{-19}$ coulombs), and $\mathrm{\Delta V}$ is the potential difference (1 volt). Therefore, 1 eV is equivalent to $1.6\times {10}^{-19}$ joules.

How do you convert electron volts (eV) to joules (J)?

To convert electron volts (eV) to joules (J), you use the conversion factor that 1 eV is equal to $1.6\times {10}^{-19}$ joules. The formula for the conversion is:

$E\left(J\right)=E\left(\mathrm{eV}\right)\times 1.6\times {10}^{-19}$

For example, if you have 100 eV, the energy in joules would be:

$100\times 1.6\times {10}^{-19}=1.6\times {10}^{-17}$ joules.

What is the relationship between kinetic energy and electron volts?

The relationship between kinetic energy (KE) and electron volts (eV) is that kinetic energy can be expressed in electron volts when dealing with subatomic particles like electrons. The kinetic energy of a particle is given by the formula:

$\mathrm{KE}=\frac{1}{2}\mathrm{mv}{2}^{}$

where $m$ is the mass of the particle and $v$ is its velocity. When the kinetic energy is given in eV, it can be converted to joules using the conversion factor:

$\mathrm{KE}\left(J\right)=\mathrm{KE}\left(\mathrm{eV}\right)\times 1.6\times {10}^{-19}$

This allows for the calculation of velocity or other parameters using standard physics equations.

How do you calculate the speed of an electron given its kinetic energy in electron volts?

To calculate the speed of an electron given its kinetic energy in electron volts (eV), you first need to convert the kinetic energy to joules (J). Use the conversion factor:

$\mathrm{KE}\left(J\right)=\mathrm{KE}\left(\mathrm{eV}\right)\times 1.6\times {10}^{-19}$

Then, use the kinetic energy formula:

$\mathrm{KE}=\frac{1}{2}\mathrm{mv}{2}^{}$

Rearrange to solve for velocity $v$:

$v=\sqrt{\frac{2\times \mathrm{KE}}{m}}$

For example, if the kinetic energy is 100 eV, convert it to joules:

$100\times 1.6\times {10}^{-19}=1.6\times {10}^{-17}$ J

Then, use the mass of the electron $9.11\times {10}^{-31}$ kg to find the speed:

$v=\sqrt{\frac{2\times 1.6\times {10}^{-17}}{9.11}}=5.93\times {10}^6$ m/s

Why is the electron volt (eV) a useful unit in particle physics?

The electron volt (eV) is a useful unit in particle physics because it provides a convenient way to express the extremely small amounts of energy associated with subatomic particles. Since 1 eV is equivalent to $1.6\times {10}^{-19}$ joules, it simplifies calculations and comparisons in the context of atomic and particle interactions. Using eV allows physicists to avoid dealing with cumbersome scientific notation and makes it easier to communicate and understand energy levels, binding energies, and reaction thresholds in experiments and theoretical models. Additionally, eV is directly related to the potential difference experienced by charged particles, making it particularly relevant for describing phenomena in electric fields.